Early warning indicators via latent stochastic dynamical systems (2309.03842v3)
Abstract: Detecting early warning indicators for abrupt dynamical transitions in complex systems or high-dimensional observation data is essential in many real-world applications, such as brain diseases, natural disasters, and engineering reliability. To this end, we develop a novel approach: the directed anisotropic diffusion map that captures the latent evolutionary dynamics in the low-dimensional manifold. Then three effective warning signals (Onsager-Machlup Indicator, Sample Entropy Indicator, and Transition Probability Indicator) are derived through the latent coordinates and the latent stochastic dynamical systems. To validate our framework, we apply this methodology to authentic electroencephalogram (EEG) data. We find that our early warning indicators are capable of detecting the tipping point during state transition. This framework not only bridges the latent dynamics with real-world data but also shows the potential ability for automatic labeling on complex high-dimensional time series.
- Vampnets for deep learning of molecular kinetics. Nat. Commun., 9(1):5, 2018.
- The tipping times in an arctic sea ice system under influence of extreme events. Chaos, 30(6):063125, 2020.
- Integrated information as a common signature of dynamical and information-processing complexity. Chaos, 32(1), 2022.
- Learning effective dynamics from data-driven stochastic systems. Chaos, 33(4), 2023.
- T. Berry and T. Sauer. Local kernels and the geometric structure of data. Appl. Comput. Harmon. Anal., 40(3):439–469, 2016.
- R. R. Coifman and S. Lafon. Diffusion maps. Appl. Comput. Harmon. Anal., 21(1):5–30, 2006.
- Diffusion maps, spectral clustering and reaction coordinates of dynamical systems. Appl. Comput. Harmon. Anal., 21(1):113–127, 2006.
- Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model. Simul., 7(2):842–864, 2008.
- Systematic determination of order parameters for chain dynamics using diffusion maps. PNAS, 107(31):13597–13602, 2010.
- Dynamical system classification with diffusion embedding for ecg-based person identification. Signal Process., 130:403–411, 2017.
- Data-driven modelling of brain activity using neural networks, diffusion maps, and the koopman operator. arXiv preprint arXiv:2304.11925, 2023.
- Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps. PNAS, 102(21):7426–7431, 2005.
- Manifold learning for latent variable inference in dynamical systems. IEEE Trans. Signal Processing, 63(15):3843–3856, 2015.
- Learning latent dynamics for partially observed chaotic systems. Chaos, 30(10):103121, 2020.
- J. Duan. An Introduction to Stochastic Dynamics, volume 51. Cambridge, 2015.
- Learning effective sdes from brownian dynamic simulations of colloidal particles. Mol. Syst. Des. Eng., 8:887–901, 2023.
- Y. Li and J. Duan. Extracting governing laws from sample path data of non-gaussian stochastic dynamical systems. J. Stat. Phys., 186:1–21, 2021.
- Detecting the maximum likelihood transition path from data of stochastic dynamical systems. Chaos, 30(11):113124, 2020.
- Dynamical inference for transitions in stochastic systems with α𝛼\alphaitalic_α-stable lévy noise. J. Phys. A Math. Theor., 49, 2015.
- Identifying early-warning signals of critical transitions with strong noise by dynamical network markers. Sci. Rep., 5(1):17501, 2015.
- Deep learning for early warning signals of tipping points. PNAS, 118(39):e2106140118, 2021.
- F. Chung. Spectral graph theory, volume 92. Am. Math. Soc., 1997.
- Stéphane S Lafon. Diffusion maps and geometric harmonics. Yale University, 2004.
- Learning effective stochastic differential equations from microscopic simulations: Linking stochastic numerics to deep learning. Chaos, 33(2), 2023.
- An end-to-end deep learning approach for extracting stochastic dynamical systems with α𝛼\alphaitalic_α-stable lévy noise. Chaos, 32(6), 2022.
- L. Onsager and S. Machlup. Fluctuations and irreversible processes. Phys. Rev., 91(6):1505, 1953.
- Physiological time-series analysis using approximate entropy and sample entropy. Am. J. Physiol. Heart Circ. Physiol., 278(6):H2039–H2049, 2000.
- Complexity-based approach for el niño magnitude forecasting before the spring predictability barrier. PNAS, 117(1):177–183, 2020.
- Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem., 53:291–318, 2002.
- Parsimonious representation of nonlinear dynamical systems through manifold learning: A chemotaxis case study. Appl. Comput. Harmon. Anal., 44(3):759–773, 2018.
- Geometric harmonics: a novel tool for multiscale out-of-sample extension of empirical functions. Appl. Comput. Harmon. Anal., 21(1):31–52, 2006.
Sponsor
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.